In this paper we demonstrate the methodology for parallelizing the computation of large one-dimensional discrete fast Fourier transforms (DFFTs) on multi-core Intel Xeon processors. DFFTs based on the recursive Cooley-Tukey method have to control cac
he utilization, memory bandwidth and vector hardware usage, and at the same time scale across multiple threads or compute nodes. Our method builds on single-threaded Intel Math Kernel Library (MKL) implementation of DFFT, and uses the Intel Cilk Plus framework for thread parallelism. We demonstrate the ability of Intel Cilk Plus to handle parallel recursion with nested loop-centric parallelism without tuning the code to the number of cores or cache metrics. The result of our work is a library called EFFT that performs 1D DFTs of size 2^N for N>=21 faster than the corresponding Intel MKL parallel DFT implementation by up to 1.5x, and faster than FFTW by up to 2.5x. The code of EFFT is available for free download under the GPLv3 license. This work provides a new efficient DFFT implementation, and at the same time demonstrates an educational example of how computer science problems with complex parallel patterns can be optimized for high performance using the Intel Cilk Plus framework.
Evidence is accumulating suggesting that collisionless shocks in supernova remnants (SNRs) can amplify the interstellar magnetic field to hundreds of microgauss or even milli-gauss levels, as recently claimed for SNR RX J1713.7-3946. If these fields
exist, they are almost certainly created by magnetic field amplification (MFA) associated with the efficient production of cosmic rays by diffusive shock acceleration (DSA) and their existence strengthens the case for SNRs being the primary source of galactic cosmic ray ions to the `knee and beyond. However, the high magnetic field values in SNRs are obtained exclusively from the interpretation of observations of radiation from relativistic electrons and if MFA via nonlinear DSA produces these fields the magnetic field that determines the maximum ion energy will be substantially less than the field that determines the maximum electron energy. We use results of a steady-state Monte Carlo simulation to show how nonlinear effects from efficient cosmic ray production and MFA reduce the maximum energy of protons relative to what would be expected from test-particle acceleration.
